Geodesic
Local semigroup rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1115-1118

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The description of local semigroup algebras over a field of characteristic $p$ (if $p>0$, then semigroups are assumed to be locally finite) due to J. Okninsky (1984) is transferred to semigroup rings over non-radical rings. The following statement is proved. Let $R$ be a ring, $R\ne J(R)$, $\operatorname{char}R=0$ ($\operatorname{char}R=p>1$), $S$ be a semigroup (respectively, a locally finite semigroup). The semigroup ring $R[S]$ is local [scalar local] if and only if $R$ is such a ring and $S$ is an ideal extension of a rectangular band (respectively of a completely simple semigroup over a $p$-group) by a locally nilpotent semigroup. 
@article{FPM_1995_1_4_a22,
     author = {A. Ya. Ovsyannikov},
     title = {Local semigroup rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1115--1118},
     publisher = {mathdoc},
     volume = {1},
     number = {4},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a22/}
}
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A. Ya. Ovsyannikov. Local semigroup rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1115-1118. http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a22/